So I got the Dolphin emulator3.65 three days ago and it plays amazingly well. The only problem I've encountered so far is saving my game. I played super smash bors. brawl and the starting screen prompts to save a file, but when I click it the screen just stays there. any tips to helping me save my progress.

Use the latest dev build from here: https://dolphin-emu.org/download/ (4.0-6604 as of writing)
This is an issue that has come up before: brawl first creating its save file can take a long time to create due to the way Dolphin handles it. Normally, you just wait until it finishes (which can take a while). However, since you quit during save file creation, your save file is broken. You need to delete your Brawl save data and then start over.

if you're using the netplay build (4.0-652), then it simply doesn't use any memory cards, which is why you can't save. if you use the latest build, you can still netplay and use memory cards, however you and the person you're playing with need to use identical cards.

Yeah, Wii games don't use GameCube memory cards. The problem is that saving game data is intentionally disabled for Wii games when playing netplay because it can lead to a lot of desyncs otherwise. I don't know if there is anything you can do about it.